Logarithm Practice Test Questions – Aptitude -- Free Practice

Question 1

If log₄(x² + x) − log₄(x + 1) = 2, then the value of x is:

A

2✓✗

B

3✓✗

C

16✓✗

D

8✓✗

Explanation

log₄x² + xx + 1 = 2
x(x + 1)x + 1 = 4² = 16
x = 16 (valid, since x + 1 ≠ 0)

Question 2

log_a √3 = 13, find the value of a

A

9✓✗

B

81✓✗

C

27✓✗

D

3✓✗

Explanation

log_a 3 = 13 means a^1/3 = 3
Cubing both sides: a = 3³ = 27

Question 3

log p²qr + log q²pr + log r²pq =

A

pqr✓✗

B

1pqr✓✗

C

1✓✗

D

0✓✗

Explanation

Using log A + log B + log C = log(ABC):
= log p²qr × q²pr × r²pq
= log p²q²r²p²q²r² = log 1 = 0

Question 4

If log a - b2 = 12(log a + log b), the value of a² + b² is:

A

6ab✓✗

B

8ab✓✗

C

6a²b²✓✗

D

None of these✓✗

Explanation

log a - b2 = log √ab
So a - b2 = √ab
a - b = 2√ab
Squaring both sides: (a - b)² = 4ab
a² - 2ab + b² = 4ab
a² + b² = 6ab

Question 5

The value of log_0.1 0.001 is:

A

3✓✗

B

2✓✗

C

4✓✗

D

1/3✓✗

Explanation

log_0.1 0.001 = log(10^-3)log(10^-1) = -3-1 = 3

Question 6

If log₄ x = -3/2, then x is:

A

1/8✓✗

B

1/4✓✗

C

1/2✓✗

D

1/3✓✗

Explanation

x = 4^-3/2 = 14^3/2 = 12³ = 18

Question 7

Given that log₁₀2 = x and log₁₀3 = y, the value of log₁₀120 is expressed as:

A

2x - y + 1✓✗

B

2x + y + 1✓✗

C

2x - y - 1✓✗

D

None of these✓✗

Explanation

log₁₀120 = log₁₀(4 × 3 × 10) = log₁₀4 + log₁₀3 + log₁₀10
= 2log₁₀2 + log₁₀3 + 1 = 2x + y + 1

Question 8

Given that log₁₀2 = x and log₁₀3 = y, the value of log₁₀60 is expressed as

A

x - y + 1✓✗

B

x + y + 1✓✗

C

x - y - 1✓✗

D

none of these✓✗

Explanation

log₁₀60 = log₁₀(2 × 3 × 10) = log₁₀2 + log₁₀3 + log₁₀10 = x + y + 1

Question 9

log_0.0110,000 = ?

A

2✓✗

B

-2✓✗

C

4✓✗

D

-4✓✗

Explanation

0.01 = 10^-2, and 10,000 = 10⁴
log_10^-2(10⁴) = 4 / (-2) = -2